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Re: st: slopes as outcomes?


From   SamL <saml@demog.berkeley.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: slopes as outcomes?
Date   Fri, 17 Nov 2006 14:36:31 -0800 (PST)

Robert,

Thanks a bunch for your assistance.  I really appreciate it.

Sam

On Thu, 16 Nov 2006, Roberto G. Gutierrez, StataCorp wrote:

> SamL <saml@demog.berkeley.edu> asks:
>
> > I've attempted to figure out how to specify a slopes-as-outcomes multilevel
> > model using _xtmixed- and at this point I am swirling in confusion.  I have
> > checked statalist and the manual, and cannot find an example that I am
> > confident matches my aim.  So, if my data has persons (i) nested within
> > univerities (j), and Model 1, a 2-equation model I seek to estimate, is:
>
> > Y_ij = b0 + b1_j*X1_ij + b2*X2_ij + e_ij
> > b0 = g00
> > b1_j = g10 + g11*Z1_j + u1_j
> > b2 = g20
>
> > what would be the appropriate syntax?
>
> This is equivalent to
>
>    Y_ij = g00 + g10*X1_ij + g11*X1_ij*Z1_j + u1_j*X1_ij + g20*X2_ij + e_ij
>
>         = (g00 + g10*X1_ij + g11*X1_ij*Z1_j + g20*X2_ij) + u1_j*X1_ij + e_ij
>
> fix in -xtmixed- using
>
>     . gen x1z1 = x1*z1
>     . xtmixed y x1 x1z1 x2 || university: x1, noconstant
>
> Note the -noconstant- option.  This is because you have a random slope on
> -x1-, but no random intercept.
>
> > And, if Model 2 has a slightly different specification:
>
> > Y_ij = b0_j + b1*X1_ij + b2*X2_ij + e_ij
> > b0 = g00 + g01*Z1_j + u0_j
> > b1 = g10
> > b2 = g20
>
> This implies
>
>    Y_ij = g00 + g01*Z1_j + u0_j + g10*X1_ij + g20*X2_ij + e_ij
>
>         = g00 + g01*Z1_j + g10*X1_ij + g20*X2_ij + u0_j + e_ij
>
> fitted as
>
>      . xtmixed y z1 x1 x2 || university:
>
> i.e., as a random-intercept (at the university level) model.
>
> They key is to manipulate your multilevel specification so that it reads as
> fixed effects part + random effects part.
>
> --Bobby
> rgutierrez@stata.com
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>
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